From 5a93af1b6a5083c236fa7328a44962a8fe983606 Mon Sep 17 00:00:00 2001
From: MaxRev-Dev <cmthea32@gmail.com>
Date: Tue, 29 Oct 2019 19:49:22 +0200
Subject: [PATCH] added cartesian product

---
 BinaryRelations/Matrix/MatrixExtensions.cs    | 41 ++++++++++
 BinaryRelationsTests/MatrixOperationsTests.cs | 76 +++++++++++++++++++
 README.md                                     |  2 +
 3 files changed, 119 insertions(+)

diff --git a/BinaryRelations/Matrix/MatrixExtensions.cs b/BinaryRelations/Matrix/MatrixExtensions.cs
index 67ce190..01bf6a7 100644
--- a/BinaryRelations/Matrix/MatrixExtensions.cs
+++ b/BinaryRelations/Matrix/MatrixExtensions.cs
@@ -1,5 +1,6 @@
 using System;
 using System.Collections.Generic;
+using System.Linq;
 using System.Linq.Expressions;
 using System.Runtime.CompilerServices;
 
@@ -548,5 +549,45 @@ private static void ThrowIfSizeNotEqual<T>(this T[,] array1, in T[,] array2)
         }
 
         #endregion
+
+        #region Combinatorics
+
+        public static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences)
+        {
+            IEnumerable<IEnumerable<T>> emptyProduct = new[] { Enumerable.Empty<T>() };
+            return sequences.Aggregate(
+                emptyProduct,
+                (accumulator, sequence) =>
+                    from acc in accumulator
+                    from item in sequence
+                    select acc.Concat(new[] { item }));
+        }
+
+        public static IEnumerable<IEnumerable<IEnumerable<int>>> CartesianProductDistinctPairs(int size, int start = 1)
+        {
+            var range = Enumerable.Range(start, size).ToArray();
+            for (var i = 1; i <= size; i++)
+                yield return Permutations(range, i);
+        }
+
+        public static IEnumerable<IEnumerable<T>> Permutations<T>(IEnumerable<T> array, int elementsInArray)
+        {
+            var range = array as T[] ?? array.ToArray();
+            var i = 1;
+            foreach (var item in range)
+            {
+                if (elementsInArray == 1)
+                {
+                    yield return new[] { item };
+                }
+                else
+                {
+                    foreach (var result in Permutations(range.Skip(i++), elementsInArray - 1))
+                        yield return new[] { item }.Concat(result);
+                }
+            }
+        }
+
+        #endregion
     }
 }
\ No newline at end of file
diff --git a/BinaryRelationsTests/MatrixOperationsTests.cs b/BinaryRelationsTests/MatrixOperationsTests.cs
index 7a7ba8c..0575287 100644
--- a/BinaryRelationsTests/MatrixOperationsTests.cs
+++ b/BinaryRelationsTests/MatrixOperationsTests.cs
@@ -1,3 +1,5 @@
+using System.Collections.Generic;
+using System.Linq;
 using BinaryRelationsTests.Helpers;
 using MaxRev.Extensions.Binary;
 using MaxRev.Extensions.Matrix;
@@ -83,5 +85,79 @@ public void SubtractMatrices()
             };
             Assert.Equal(expected, m1.Subtract(m2));
         }
+
+        [Fact]
+        public void Permutations()
+        {
+            var expected = new[]
+            {
+                new[] {1, 2, 3},
+                new[] {1, 2, 4},
+                new[] {1, 2, 5},
+                new[] {1, 3, 4},
+                new[] {1, 3, 5},
+                new[] {1, 4, 5},
+                new[] {2, 3, 4},
+                new[] {2, 3, 5},
+                new[] {2, 4, 5},
+                new[] {3, 4, 5},
+            };
+            Assert.Equal(expected, MatrixExtensions.Permutations(Enumerable.Range(1, 5), 3));
+        }
+
+        [Fact]
+        public void CartesianProductDistinctPairs()
+        {
+            var expected = new[] {
+                new[]
+                {
+                    new[] {1},
+                    new[] {2},
+                    new[] {3},
+                    new[] {4},
+                    new[] {5},
+                },
+                new[]
+                {
+                    new[] {1, 2},
+                    new[] {1, 3},
+                    new[] {1, 4},
+                    new[] {1, 5},
+                    new[] {2, 3},
+                    new[] {2, 4},
+                    new[] {2, 5},
+                    new[] {3, 4},
+                    new[] {3, 5},
+                    new[] {4, 5},
+                },
+                new[]
+                {
+                    new[] {1, 2, 3},
+                    new[] {1, 2, 4},
+                    new[] {1, 2, 5},
+                    new[] {1, 3, 4},
+                    new[] {1, 3, 5},
+                    new[] {1, 4, 5},
+                    new[] {2, 3, 4},
+                    new[] {2, 3, 5},
+                    new[] {2, 4, 5},
+                    new[] {3, 4, 5},
+                },
+                new[]
+                {
+                    new[] {1, 2, 3, 4},
+                    new[] {1, 2, 3, 5},
+                    new[] {1, 2, 4, 5},
+                    new[] {1, 3, 4, 5},
+                    new[] {2, 3, 4, 5},
+                },
+                new []
+                {
+                   new[] {1, 2, 3, 4, 5}
+                }
+            };
+
+            Assert.Equal(expected, MatrixExtensions.CartesianProductDistinctPairs(5));
+        }
     }
 }
\ No newline at end of file
diff --git a/README.md b/README.md
index 78ea4d8..c03f4d0 100644
--- a/README.md
+++ b/README.md
@@ -60,3 +60,5 @@ Provides a bunch of extension methods for binary matrices including:
 	- Randomize
 	- AllocateRandomSquareMatrix
 	- AllocateRandomVector
+	- CartesianProduct
+	- CartesianProductDistinctPairs